The problem is that Denmark would be responsible for defending it, and logistically, that would be a nightmare. There is basically no efficient way to ship an army there without crossing US-controlled territory, be it via land (impossible), sea (US took back control of the Panama canal, remember?), or air (minimum 12 hour nonstop flight, and that's only if you're crossing US airspace).

On top of that, Denmark only has 6 Million people, so even if they shipped literally all of their soldiers there it probably wouldn't be enough to realistically hold it against a US invasion. Trump could simply order the US military to take it back and they'd likely finish the job in less than a week. Sure, Denmark could draw from the local population and invest in massive military training programs, but that would take years to accomplish and likely cost a good chunk of even their combined GDP (which they've already pledged to universal healthcare and a free Danish cookies).